Robust stabilization of a class of linear discrete-time time-varying systems: A LMI approach

The stabilization problem of a linear, discrete-time, time-varying, uncertain system is considered and a numerically efficient method for its solution is proposed. The elements of the dynamical matrix of the system are modelled as unknown time functions taking values inside known compact intervals. The measure and the control matrices are assumed to be known and time-invariant. It is required to find a linear, time-invariant, dynamic output controller yielding a uniformly, asymptotically stable closed-loop system. The problem solvability conditions are stated in terms of feasibility of a set of LMI's, which is independent of the number of uncertain parameters